Distributionally Conservative Stochastic Dominance via Subsampling

ABSTRACT This note defines distributionally conservative versions of stochastic dominance relations based on subsampling. It presents a non‐asymptotic analysis of the probability of the false dominance (FD) error for the empirical version of the subsampling‐based empirical dominance procedure. The analysis is based on the generalization of the McDiarmid's concentration inequality to ‐mixing processes by Kontorovich and Ramanan. The concentration bounds obtained depend on the entropy characteristics of the problem, such as the Lipschitz coefficients of the utilities involved, the FD parameters involved, and the coefficients that represent temporal dependence at each subsample. The analysis establishes tighter concentration bounds for the conservative procedure in both stationary and nonstationary cases when the subsampling rate is appropriately chosen.